106 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



tion on the axis, we shall clearly have a measure of this relative varia- 

 bility. I have done this for all of the tables, but since it is evident, if 

 in an expression 



100 (r 



^ = ir 



o- is decreasing while M is increasing in value, that v must also decrease, 

 it does not seem worth while reproducing these coefficients in detail. 

 In order to afford some idea of how the actual values run, however, 

 there are given in table 53 the coefficients of variation for the first four 

 whorls on primary branches in Series I, II, and III and IV, and on all 

 branches in Series V and VI. 



Table 55. — Coefficients of variation for successive whorls of primary branches. 



We see in all the series that while the branches start with a relatively 

 very variable first whorl, the variability rapidly decreases in the suc- 

 ceeding ones. The same thing is shown if we calculate the coefficients 

 of variation for secondary-branch whorls. 



SUMMARY OF SECTION. 



In this section of the paper it has been shown that both absolutely 

 and in proportion to the size the variability of successive whorls in 

 respect to leaf-number diminishes as we pass from the most proximal 

 to the most distal whorl on an axial division. This relation has been 

 demonstrated for the three most important axial divisions (main stem, 

 primary and secondary branches), and it can not reasonably be doubted 

 that it also holds in the same way for the other divisions (tertiary and 

 quaternary branches) . But from the method of growth of Ceratophyl- 

 lum we know that succession of whorls in position on the branch 

 denotes succession in order of formation or differentiation from the 

 growing bud. Our result, then, means that as whorls are successively 

 produced by a growing bud, they are formed with ever-increasing constancy 

 to their type, the ultimate limit towards which the process is tending being 

 absolute constancy. This may be designated as the "Second law of 

 growth" in Ceratophyllum. 



